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Page 1 Math 142-copyright Joe Kahlig, 15C Section Q: Quadratic Functions A parabola is a second degree polynomial that can be written in one of the following forms. y = ax2 + by + c y = a(x − h)2 + k Example: Find the following for the parabola and then sketch a rough graph. y = −2(x + 4)2 + 7 Vertex: opens: max value: min value: Example: Find the vertex and determine if the parabola crosses the x-axis. If it does, find these values of x. y = x2 − 28x + 350 Math 142-copyright Joe Kahlig, 15C Page 2 Example The price-demand function for a product is given by p = 1400 − 50x where the units of x are in thousand items and the units of p are in dollars per thousand items. The cost, in dollars, is given by C(x) = 2000 + 500x. A) Find the revenue function. B) Find the number of items that would maximize the revenue. C) Find the number of items that would maximize profit. D) What is the price per thousand items when profit is maximized? E) Find the break even values. F) Between what production levels will the company have a profit?